When an object is placed at a distance of 25 cm from a mirror, the magnification is `m_(1)`. The object is moved 15cm farther away with respect to the earlier position, and the magnification becomes `m_(2)`. If `m_(1)//m_(2)=4` , then calculate the focal length of the mirror.

Options

A. 5 cm
B. 10 cm
C. 15 cm
D. 20 cm

Answer

D

Explanation

Since ` ( m _ 1 ) /( m _ 2 ) = 4`, therefore ` ( f + 40 ) /( f + 25 ) = 4 `
thus ` f + 40 = 4 f + 100`
or ` f = - 20 cm `
The negative sign shows that the mirror is concave.